本项目旨在探讨正倒向随机微分方程驱动的次优控制及其相关问题。基于值函数非光滑性质，项目借助于粘性解理论来刻画在次优轨道下值函数、伴随方程以及哈密尔顿函数之间的关系。与经典情形不同，此时定义的粘性解含有摄动因子。此外，我们研究相应的次优控制验证定理，这个定理在构造次优反馈控制方面发挥重要作用。最后，项目将探讨正倒向随机系统次优控制在金融等领域的应用并提供线性递归效应的例子。

This project focuses on near optimal control for systems governed by forward-backward stochastic differential equations (FBSDEs for short) and related topics. Since the nonsmoothness is inherent in this subject, viscosity approach is employed to investigate the relationships among the value function, the adjoint equations and Hamiltonian along optimal trajectories. Unlike the classical case, the definition of viscosity solution contains certain perturbation factor. In addition, we study the near optimal control verification theorem which plays an important role in constructing near optimal feedback control. At last, we will discuss the near optimal control of FBSDEs applied in financial fields. As an application, a kind of stochastic recursive near optimal control problem is given to illustrate our theoretical results as well.